DAnteils

DAnteils is a term used in data analysis and related fields to denote the set of shares that collectively account for the total value of a measured quantity across different components or categories. It is commonly employed to summarize how a quantity is distributed among parts of a whole, such as market segments, demographic groups, or resource allocations.

Formally, suppose there are k categories with nonnegative values s1, s2, ..., sk representing the quantity in each category. The DAnteils for category i is defined as ai = si divided by the sum of all category values, S = sum_j sj. The resulting DAnteils vector (a1, a2, ..., ak) has nonnegative components that sum to 1. When expressed as percentages, the components sum to 100%. The measure is invariant to uniform scaling of all category values.

Properties and use cases: DAnteils provides a concise snapshot of composition, emphasizing relative importance rather than absolute size. It is useful in comparing distributions across groups, visualizing market shares, voting shares, or resource allocation. It is often presented alongside other descriptive statistics to convey both the magnitude and the pattern of distribution.

Relation to other concepts: While closely related to simple proportions or shares, DAnteils is distinct from dispersion or inequality measures such as the Gini coefficient. It complements entropy-based or Theil-like indices by focusing on the proportional composition of a total.

Etymology and usage: The term appears primarily in German-language or cross-cultural texts as a label for distribution shares. Authors may use synonyms such as Anteil, Proportion, or Anteilsmultiples depending on context.